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3 years ago

Michael is running for president. The proportion of voters who favor Michael is 0.8. A random sample of 100 voters is taken.

Mathematics

1 answer:

Anton [14]3 years ago

5 0

Answer:

Michael is running for president. The proportion of voters who favor him is 0.3. A simple random sample of 100 voters is taken.

What is the expected value :: n*p = 100*0.8 = 80

standard deviation:: sqrt(n*p*q) = sqrt(80*0.2) = 16

where q is proportion of voters who do not favor Michael. (q=0.2)

and shape of the sampling distribution is binomial distribution which is approximately a bell shaped.

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what is the probability that the number of voters in the sample who will not favor Michael will be more than 16

P(X < 16.0) = P((x - 20) / 4.0) < (16.0 - 20) / 4.0) = P(Z < -1.00) = .1587

P(X > 16.0) = 1 - 0.1587 = 0.8413

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Tell whether the ordered pair is a solution of the given system. (-2,-4) {y=1/2x -3, y=-2x-8}

kompoz [17]

Answer:

The ordered pair $(-2,\, -4)$ is indeed a solution to the system:

$\left\lbrace\begin{aligned} & y = \frac{1}{2}\, x - 3 \\ & y = -2\, x - 8\end{aligned}\right.$ .

Step-by-step explanation:

Consider a system of equations about variables $x$ and $y$ . An ordered pair $(x_{0},\, y_{0})$ (where $x_{0}$ and $y_{0}$ are constant) is a solution to that system if and only if all equations in that system hold after substituting in $x = x_{0}$ and $y = y_{0}$ .

For the system in this question, $(-2,\, -4)$ would be a solution only if both equations in the system hold after replacing all $x$ in equations of the system with $(-2)$ and all $y$ with $(-4)$ .

The $\texttt{LHS}$ of the equation $y = (1/2)\, x - 3$ would become $(-4)$ . The $\texttt{RHS}$ of that equation would become $(1/2) \, (-2) - 3$ . The two sides are indeed equal.

Similarly, the $\texttt{LHS}$ of the equation $y = -2\, x - 8$ would become $(-4)$ . The $\texttt{RHS}$ of that equation would become $(-2)\, (-2) - 8$ . The two sides are indeed equal.

Thus, $x = (-2)$ and $y = (-4)$ simultaneously satisfy both equations of the given system. Therefore, the ordered pair $(-2,\, -4)$ would indeed be a solution to that system.

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2 years ago

Colton has a stone paperweight composed of a triangular pyramid on top of a triangular prism with the dimensions shown below. Us

Eva8 [605]

The area of the base would be found using the area of a triangle formula which is 1/2 x base x height.

The base and height are the two sides perpendicular to each other, which are both 5 inches.

The area of the base = 1/2 x 5 x 5 = 12.5 square inches.

The volume of the triangular prism is the area of the base times the height, which is 4 inches.

Volume of the triangular prism is 12.5 x 4 = 50 cubic inches.

Volume of the triangular prism is 1/3 x area of base x height, which is 7:

Volume of the triangular prism = 1/3 x 12.5 x 7 = 29.17 cubic inches.

Total volume = 29.17 + 50 = 79.17 cubic inches.

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3 years ago

This isosceles triangle has two sides of equal length , a, that are longer than the length of the base , b. The perimeter of the

Sholpan [36]

We are give the equation of the perimeter of the triangle as follows:
2a + b = 15.7
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Now, if we want to calculate the length of the base, all we have to do is isolate the b in one side of the equation as follows:
b = 15.7 - 2a

We know that a = 6.3 cm, therefore, the length of the base can be calculated as follows:
b = 15.7 - 2(6.3) = 3.1 cm

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3 years ago

If George received $78.00 for his work and he gets paid 6 dollars and hour how much is he getting paid

swat32

13 hours 78÷6=13 hope it helps

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3 years ago

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(2a^2-5)+(3a^2-6a+3)

Ne4ueva [31]

Answer:

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